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Motivated by observations of turbulence in the strongly stratified ocean thermocline, we use direct numerical simulations to investigate the interaction of a sinusoidal shear flow and a large-amplitude internal gravity wave. Despite strong…
We consider the spectral transfers of sign-definite invariants in general wave turbulence systems equipped with a wave kinetic equation. We develop a formalism to investigate and to characterize these transfers, based on the ability to…
The energy gradient theory was proposed in our previous studies. The mechanism of flow instability is very different in shear driven flows from pressure driven flows. In present paper, the relationship for the energy variation, work done,…
We present a mathematical description of turbulent entrainment that is applicable to free shear problems that evolve in space, time or both. Defining the global entrainment velocity $\overline V_g$ to be the fluid motion across an…
Even though the energy carried by a gravitational wave is not itself gauge invariant, the interaction with a gravitational antenna of the gravitational wave which carries that energy is. It therefore has to be possible to make some…
Although internal gravity waves are generally recognized as an important mechanism to distribute energy through the atmosphere, their dynamics near the instability is only partially understood to date. Many types of instabilities, notably…
Gaussian measures of Gibbsian type are associated with some shell models of 3D turbulence; they are constructed by means of the energy, a conserved quantity for the 3D inviscid and unforced shell model. We prove the existence of a unique…
A linearly unstable, sinusoidal $E \times B$ shear flow is examined in the gyrokinetic framework in both the linear and nonlinear regimes. In the linear regime, it is shown that the eigenmode spectrum is nearly identical to hydrodynamic…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
A theoretical analysis is presented for turbulent flows, applicable for canonical (channel, boundary-layer and free jet) geometries. Momentum and energy balance for a control volume moving at the local mean velocity decouples the…
We present a new general method to construct an action functional for a non-potential field theory. The key idea relies on representing the governing equations of the theory relative to a diffeomorphic flow of curvilinear coordinates which…
Despite recent progress, laminar-turbulent coexistence in transitional planar wall-bounded shear flows is still not well understood. Contrasting with the processes by which chaotic flow inside turbulent patches is sustained at the local…
Identifying generic physical mechanisms responsible for the generation of magnetic fields and turbulence in differentially rotating flows is fundamental to understand the dynamics of astrophysical objects such as accretion disks and stars.…
We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
We investigate the dynamics of microcapsules in linear shear flow within a reduced model with two degrees of freedom. In previous work for steady shear flow, the dynamic phases of this model, i.e. swinging, tumbling and intermittent…
Internal waves in the ocean interact in triads. Early work emphasized the importance of extreme-scale separated interactions in which two large wavenumber waves interact with one small wavenumber wave. More recent efforts have called this…
We demonstrate via direct numerical simulations that a periodic, oscillating mean flow spontaneously develops from turbulently generated internal waves. We consider a minimal physical model where the fluid self-organizes in a convective…
In this work, we discuss a situation which could lead to both wave turbulence and collective behavior kinetic equations. The wave turbulence kinetic models appear in the kinetic limit when the wave equations have local differential…
We formulate multifractal models for velocity differences and gradients which describe the full range of length scales in turbulent flow, namely: laminar, dissipation, inertial, and stirring ranges. The models subsume existing models of…